Phase modulation schemes are very effective and are therefore widely used in communication systems. A simple example of a phase modulation scheme is quaternary phase shift keying (QPSK). This modulation scheme maps two-bit digital data to one of four phase offsets as shown in FIG. 1a. Ideally, the trajectory of the complex signal intersects these symbols at periodic points in time. In practice, pulse-shaping filters—needed to constrain the frequency spectrum of the signal—introduce some variations as illustrated by FIG. 1b. 
FIG. 2 shows a typical QPSK (or I/Q) modulator used to generate the complex phase-modulated signal. This technique relies on orthogonal signal vectors to realize the phase offsets—an inherently linear technique, since it depends solely on the matching of these orthogonal signals.
The I/Q modulator provides a straightforward approach to generating phase-modulated signals. But, it's also possible to generate the phase-modulated signals using a polar transmitter such as the one shown in FIG. 3. This approach reduces circuitry, lowers power consumption, and potentially supports multiple modulation formats. It separately applies the phase and amplitude signals with precise alignment to realize the complex QPSK modulation. Unfortunately, several factors make this alignment very difficult. It would therefore be advantageous to be able to precisely align the phase and amplitude modulation signals.